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1 – 10 of over 2000D. Dutta Majumder and Kausik Kumar Majumdar
In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature…
Abstract
In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature. Fuzzy real numbers, fuzzy logic, possibility theory, probability theory, Dempster‐Shafer theory, artificial neural nets, neuro‐fuzzy, fractals and multifractals, etc. are some of the paradigms to help us to understand complex systems. We present a very detailed discussion on the mathematical theory of fuzzy dynamical system (FDS), which is the most fundamental theory from the point of view of evolution of any fuzzy system. We have made considerable extension of FDS in this paper, which has great practical value in studying some of the very complex systems in society and nature. The theories of fuzzy controllers, fuzzy pattern recognition and fuzzy computer vision are but some of the most prominent subclasses of FDS. We enunciate the concept of fuzzy differential inclusion (not equation) and fuzzy attractor. We attempt to present this theoretical framework to give an interpretation of cyclogenesis in atmospheric cybernetics as a case study. We also have presented a Dempster‐Shafer's evidence theoretic analysis and a classical probability theoretic analysis (from general system theoretic outlook) of carcinogenesis as other interesting case studies of bio‐cybernetics.
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Focuses on the applications of fuzzy set theory as a tool for the construction of multi‐criteria decision functions from specifications expressed in natural language. Starting…
Abstract
Focuses on the applications of fuzzy set theory as a tool for the construction of multi‐criteria decision functions from specifications expressed in natural language. Starting with the ability to represent individual criteria satisfactions in terms of membership of fuzzy subsets, shows how different types of linguistic specifications are implemented. Consideration is given to the representation of trade‐offs between criteria, quantifier‐guided aggregations, conditioned criteria and possibilistically qualified criteria.
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We investigated a fuzzy programming problem in which the constraints are a fuzzy subset over the alternatives and the objective is in the form of a linear ordering. A fuzzy subset…
Abstract
We investigated a fuzzy programming problem in which the constraints are a fuzzy subset over the alternatives and the objective is in the form of a linear ordering. A fuzzy subset is developed which reflects the objects ranking information in terms of grades of membership of the constraints. These two fuzzy subsets then are combined via intersection operation to form a fuzzy decision function.
We introduce a general definition for prototypical operators, such as the mean of a set of elements. We investigate the properties of this operator. We extend the definition to…
Abstract
We introduce a general definition for prototypical operators, such as the mean of a set of elements. We investigate the properties of this operator. We extend the definition to find prototypical elements of fuzzy sets. We study this operators effect on Zadeh's definition of “very.”
D.S. Malik and John N. Mordeson
In this paper, we define and examine the concept of a fuzzy recognizer. If L(M) is the language recognized by an incomplete fuzzy recognizer M, we show that there is a completion M…
Abstract
In this paper, we define and examine the concept of a fuzzy recognizer. If L(M) is the language recognized by an incomplete fuzzy recognizer M, we show that there is a completion M of M such that L(M) = L(M). We also show that if A is a recognizable set of words, then there is a complete accessible fuzzy recognizer MA such that L(MA) = A. We lay groundwork to determine rational decompositions of recognizable sets.
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Osman Taylan and Ibrahim A. Darrab
The purpose of this paper is to demonstrate the use of artificial intelligence methods in quality control and improvement. The paper introduces a systematic approach for the…
Abstract
Purpose
The purpose of this paper is to demonstrate the use of artificial intelligence methods in quality control and improvement. The paper introduces a systematic approach for the design of fuzzy control charts of tip shear carpets.
Design/methodology/approach
There are certain steps for designing fuzzy control charts. All input, state and output variables of the carpet plant and partition of the universe of discourse were first determined. The interval spanned by each variable and the number of fuzzy subsets each assigned with a linguistic label were identified. Then, the adaptive capability of neural network was used to determine the membership functions for each fuzzy subset. The fuzzy relationship functions between the inputs and outputs were assigned to form the fuzzy rule base (controller) in order to normalize the variables and certain intervals. Fuzzification of input parameters and max‐min composition of rules for inferring crisp outputs was the next step. The aggregation of fuzzified outputs and defuzzification of the outputs were the last step of this study, which helped to produce crisp outputs for latex weight.
Findings
Fuzzy linguistic terms were employed for overall quality assessment and rating of the end product. The outcomes of neuro‐fuzzy system were good supplements to other statistical process control tools.
Research limitations/implications
Lack of qualified domain experts, knowledge acquisition of process parameters and time limitation for training of neuro‐fuzzy model were primary limitations.
Practical implications
The approach is more flexible and meaningful to identify the quality distribution of a product. The qualitative aspect of human reasoning for decision making was employed in this approach.
Originality/value
The paper is original and the first such work for local industry.
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This work aims to ask for the possibility to establish one or more Europes in a heterogeneous territory where the main goal is to create a common space. The use of a specific…
Abstract
Purpose
This work aims to ask for the possibility to establish one or more Europes in a heterogeneous territory where the main goal is to create a common space. The use of a specific methodology will help us to know whether it is possible to apply general policies in the whole territory or it will be necessary to adapt them to a different group of spaces.
Design/methodology/approach
Taking into account the experts’ opinions, causality relationships, grouping processes and distances techniques can be obtained to get an overall view of different groups of areas where it will be possible to develop the specific policies successfully.
Findings
Theoretically, the proposed model using fuzzy logic in grouping processes presents significant results that contribute to the theory on regional development.
Originality/value
This paper provides a new approach to solve the territorial problem to apply the European policies. Introducing these techniques, one will be able to approach the different positions to the specific areas in Europe to create a peaceful and harmonic space of cohabitation.
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Two solution concepts for a FMP problem are suggested. The first one makes use of level sets of the fuzzy set of feasible alternatives. The second solution is based on the concept…
Abstract
Two solution concepts for a FMP problem are suggested. The first one makes use of level sets of the fuzzy set of feasible alternatives. The second solution is based on the concept of Pareto maximum in vector optimization. It is shown that both solutions are equivalent in a sense that they give the same fuzzy value of a function maximized. It is suggested that if a decision‐maker is to choose a single element, then his choice must be based not only on the membership value of this element in the solution fuzzy set but also on the corresponding value of the function maximized. In this respect the situation is similar to that typical for vector optimization. The approach suggested in this paper is further used for analysing games with fuzzy sets of strategies of the players. A fuzzy equilibrium solution is introduced, which can provide a base for an agreement between the players.
This brief paper considers the various possible mathematical operations on fuzzy sets that are required to implement a set of control rules as a fuzzy logic control element. The…
Abstract
This brief paper considers the various possible mathematical operations on fuzzy sets that are required to implement a set of control rules as a fuzzy logic control element. The influence that these operations have on the characteristics of the final control element is a factor that is used to select those operations most suitable in the control context.
Intends to address a fundamental problem in maintenance engineering: how should the shutdown of a production system be scheduled? In this regard, intends to investigate a way to…
Abstract
Purpose
Intends to address a fundamental problem in maintenance engineering: how should the shutdown of a production system be scheduled? In this regard, intends to investigate a way to predict the next system failure time based on the system historical performances.
Design/methodology/approach
GM(1,1) model from the grey system theory and the fuzzy set statistics methodologies are used.
Findings
It was found out that the system next unexpected failure time can be predicted by grey system theory model as well as fuzzy set statistics methodology. Particularly, the grey modelling is more direct and less complicated in mathematical treatments.
Research implications
Many maintenance models have developed but most of them are seeking optimality from the viewpoint of probabilistic theory. A new filtering theory based on grey system theory is introduced so that any actual system functioning (failure) time can be effectively partitioned into system characteristic functioning times and repair improvement (damage) times.
Practical implications
In today's highly competitive business world, the effectively address the production system's next failure time can guarantee the quality of the product and safely secure the delivery of product in schedule under contract. The grey filters have effectively addressed the next system failure time which is a function of chronological time of the production system, the system behaviour of near future is clearly shown so that management could utilize this state information for production and maintenance planning.
Originality/value
Provides a viewpoint on system failure‐repair predictions.
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